International Symposium on Stochastic Models in Reliability Engineering, Life Sciences and Operations Management (SMRLO'10)
PRODUCTIVITY ASSESSMENT AND IMPROVEMENT MEASUREMENT OF DECISION MAKING UNITS - AN APPLICATION FOR RANKING CITIES IN ISRAEL
Yossi HADAD Prof., Industrial Engineering and Management Department, SCE - Shamoon College of Engineering, Beer-Sheva, Israel
E-mail:
[email protected]
Baruch KEREN PhD, Industrial Engineering and Management Department, SCE - Shamoon College of Engineering, Beer-Sheva, Israel
E-mail:
[email protected]
Avner BEN-YAIR PhD, Center for Reliability and Risk Management, SCE - Shamoon College of Engineering, Beer-Sheva, Israel
E-mail:
[email protected]
Abstract: In this paper we will demonstrate how productivity and improvement rate of urban organizational units (called also Decision Making Units - DMU's) may be assessed when measured along several time periods. The assessment and subsequent ranking of cities is achieved by means of the Data Envelopment Analysis (DEA) methodology to determine DMU's efficiency for each period, the Cross Efficiency ranking method to rank DMU's and the Malmquist Index approach which measures changes in productivity relative to a base period. The above combined methodology will be applied to a case study of 70 Israeli cities in years 2006, 2007 and 2008.
Key words: Data Envelopment Analysis (DEA); Malmquist Index; ranking methods
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International Symposium on Stochastic Models in Reliability Engineering, Life Sciences and Operations Management (SMRLO'10) 1. Introduction Banks, insurance companies, widespread food chains, police stations, etc., are organizations that have several branches and subunits (Decision Making Units - DMUs). Such organizations are often interested in assessing the productivity of their DMU's in two main aspects: 1) Relative efficiency of each DMU per every time period; 2) General improvement trends among DMU's. The importance of this assessment boils down to first know better relative productivity of each DMU as compared to other structural units, and in addition to be aware of improvement trends characteristic of every DMU. Profound knowledge of the above parameters enables decision makers in the regarded organizations to assess better specific performance of each division unit as well as their timely changes, thus contributing to a broader managerial view on every DMU within the organization. In our application we assume that cities are subunits of the organization, and therefore their relative productivities and their improvement trends should be estimated. Relative efficiency of each DMU (productivity assessment) for every time period may be investigated by means of the DEA methodology (the so-called CCR or BCC models) which have been primarily suggested by Charnes, Cooper and Rhodes (CCR) in 1978 and subsequently developed and expanded by Banker, Charnes and Cooper (BCC) in 1984. The CCR model calculates the Technical and Scale Efficiency (TSE) while BCC determines Technical Efficiency (TE). In addition to that, productivity assessment may be facilitated by means of conventional ranking methods, like the Super Efficiency method (SE) developed by Anderson and Peterson (1993), the Cross Efficiency method (CE) introduced by Sexton et al. (1994), the bi-criteria method for efficient DMU ranking suggested by Hadad and Friedman (2004), as well as a combination of the AHP method (Analytical Hierarchic Process) and the DEA methodology described by Sinuany-Stern et al. (2000). A comprehensive review of contemporary ranking methods can be found in a study by Adler et al. (2002). In recent years, a variety of scientific papers tackling the problem of productivity assessment by means of DEA and ranking methods, have been published and are available to the broad scientific community. Among others, one should mention Sueyoshi (1992) who measured the industrial performance of 35 Chinese cities by means of Data Envelopment Analysis, Doyle and Green (1994) who ranked 20 universities in the UK; Hadad, et al. (2009), to carry out comparative efficiency assessment and ranking of public defence authority in Israel; Malul, et al. (2009), measuring and ranking of economic, environmental and social efficiency of countries; Hadad, et al. (2007), measuring efficiency of restaurants; Hadad, et al. (2004), evaluating hotel advertisements efficiency using DEA; Hadad, et al. (2004), ranking fish farms. Relative improvement trend for each DMU may be assessed when comparing productivities determined for every pair of consecutive time periods, or by means of Malmquist Index approach primarily suggested by Caves, et al. (1982) and subsequently developed by Fare, et al. (1985) and Fare, et al. (1994). This method investigates the improvement measure of each DMU during every pair of consecutive time periods. Should the amount of time periods exceed 2, the procedure boils down to determining improvement levels for consecutive time periods with subsequently calculating the mean geometrical product for all values obtained during the regarded complex time period (Coelli, (1996)). Practical implementation of the Malmquist Index approach have been demonstrated by Barros (2006) who investigated relative efficiency of 33 police stations in Lisbon during
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International Symposium on Stochastic Models in Reliability Engineering, Life Sciences and Operations Management (SMRLO'10) 2001-2002. In his research, Barros also estimates the total productivity change of the Lisbon Police Force. In the present paper, we will demonstrate joint implementation of the DEA methodology, the Cross Efficiency ranking method and the Malmquist Index approach for productivity assessment of 70 Israeli cities between 2006-2008. The cities will be estimated every year separately upon a variety of parameters which we will regard as inputs or outputs. In addition, we will verify existence of positive correlation between the productivity ratios calculated by means of the Cross Efficiency method versus the Malmquist Index approach. Our paper is organized in the following way. The next section introduces the presentation and formulation of DEA procedures, which will be employed in the analysis and the Super Efficiency. The third section presents the Malmquist Index approach. Part four illustrates how to evaluate city advertisements’ efficiency using the models that have been described in sections two and three. Finally, the findings are presented along with conclusions and recommendations for future research.
2. Data Envelopment Analysis and Cross Efficiency 2.1. Data Envelopment Analysis DEA is a procedure designed to measure the relative efficiency in situations when there are multiple inputs and multiple outputs and no obvious objective how to aggregate both inputs and outputs into a meaningful index of productive efficiency DEA was developed by Charnes Cooper and Rhodes (CCR) (1978). The method provides a mechanism for measuring the efficiency of each Decision-Making Unit (DMU). The efficiency in CCR model is termed Technical and Scale Efficiency (TSE) and the relative efficiency of a DMU is defined as the ratio of its total weighted output to its total weighted input. The BCC model, named after Banker, Charnes and Cooper (1984) allow the production function to exhibit non-constant return to scale (Banker and Chang 1995)) whiles the CCR model imposes the additional assumption of constant returns to scale on the production function. The formulation of CCR model for unit k is: Maximize
hk =
s
∑U Y r =1
k r rk
subject to s
m
r =1
i =1
∑UrkYrj − ∑Vik Xij ≤ 0 for j = 1,2,..,n, m
∑V X i =1
k
i
ik
(1)
= 1,
Urk ≥ ε > 0
r = 1,2,..,s ,
Vik ≥ ε > 0
i = 1,2,...,m.
where ε is defined as an infinitesimal constant (a non-Archimedean quantity).
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International Symposium on Stochastic Models in Reliability Engineering, Life Sciences and Operations Management (SMRLO'10) 2.2. The Cross Efficiency The Cross Evaluation matrix was first developed by Sexton et al. (1994). This method calculated the efficiency score of each unit n times using the optimal weights evaluated by each run. The results of all the DEA cross efficiency are summarized in a matrix as given in (2) s
hkj =
∑U
k r
∑V
k
r =1 m
,
i
i =1
Yrj
j = 1,2,..., n , k = 1,2,..., n .
(2)
X ij
Thus hkj represents the score given to unit j by the optimal weights of unit k . The elements in the diagonal hkk represent the standard DEA scores hk . The Cross Efficiency ranking method utilized the matrix hkj for ranking the units one scale. Ranking of DMUs is thus based on the average cross efficiency score being calculated as n
hk =
∑h
kj
j =1
n
.
3. The Malmquist Index Approach To investigate improvement of productivity, Fare et al. (1994) have demonstrated that DEA methodology may be applied to assess Malmquist Total Factor Productivity (TFP) index numbers. As a matter of fact, Malmquist index is an approach enabling relative measurement of productivity changes between consecutive periods of time (e.g., a year). Those productivity changes may be broken down to structural elements depending on technical efficiency enhancement as well as technology changes and progress. The Malmquist DEA approach determines efficiency level in a certain year relatively to the previous one, thus enabling evaluation of productivity improvement between the two consecutive periods. The Malmquist TFP index measures efficiency in each period t related to the base period s in terms of productivity improvement. Fare et al. (1994) specifies an output based Malmquist productivity change index: 1
⎡ d s (y , x ) d t (y , x ) ⎤ 2 m0 ( y s , x s , y t , xt ) = ⎢ 0s t t × 0t t t ⎥ ⎣ d 0 ( y s , x s ) d 0 ( y s , x s )⎦
(3)
where the notations d 0 ( yt , xt ) , d 0 ( y t , xt ) , d 0 ( y s , xs ) , d 0 ( y s , x s ) are distance s
functions and x ,
t
s
t
y are the output and input vector.
An equivalent way of writing this would be 1
d t ( y , x ) ⎡ d s ( y , x ) d t ( y , x )⎤ 2 m0 ( y s , x s , y t , xt ) = 0s t t ⎢ 0s t t × 0t s s ⎥ . d 0 ( y s , x s ) ⎣ d 0 ( y t , xt ) d 0 ( y s , x s ) ⎦
(4)
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International Symposium on Stochastic Models in Reliability Engineering, Life Sciences and Operations Management (SMRLO'10) The above equation can be broken into two parts, namely the efficiency change component and the technical change component:
Efficiency change =
d 0t ( y t , xt ) d 0s ( y s , x s )
(5)
and 1
⎡ d s ( y , x ) d t ( y , x )⎤ 2 Technical change = ⎢ 0s t t × 0t s s ⎥ . ⎣ d 0 ( y t , xt ) d 0 ( y s , x s ) ⎦
(6)
The Malmquist productivity change index may be determined as the result of solving 4 linear programming problems as listed below:
⎧d 0s ( y t , xt ) = min θ ⎪ ⎪⎪subject to ⎨ − y ot + Ys λ ≥ 0 ⎪ θx − X λ ≥ 0 0t s ⎪ ⎪⎩ λ≥0 ⎧d 0t ( y t , xt ) = min θ ⎪ ⎪⎪subject to ⎨ − y os + Ys λ ≥ 0 ⎪ θx − X λ ≥ 0 0s s ⎪ ⎪⎩ λ≥0 In (7-10),
θ
is a scalar,
λ
(7)
⎧d 0s ( y s , x s ) = min θ ⎪ ⎪⎪subject to ⎨ − y os + Ys λ ≥ 0 ⎪ θx − X λ ≥ 0 0s s ⎪ ⎪⎩ λ≥0
(8)
(9)
⎧d 0t ( y t , xt ) = min θ ⎪ ⎪⎪subject to ⎨ − y ot + Yt λ ≥ 0 ⎪ θx − X λ ≥ 0 0t t ⎪ ⎪⎩ λ≥0
(10)
is a vector that representative the constants. The value
of θ will be the efficiency score for the i -th DMU. It will satisfy θ less than or equal to 1, with a value of 1 indicating a point on the frontier and hence a technically efficient DMU. These four LPs must be solved for each DMU in the sample.
4. The Case Study on Israeli Cities 4.1. Determining DMUs In order to proceed with the DEA procedure one has to determine first Decision Making Units (DMUs). In our research, we decided to determine DMUs as Israeli cities comprising a total of 10,000 inhabitants at least. The latter data has been adopted from the Central Bureau Statistics database published in 2006, 2007, 2008. 4.2. Selection of outputs and inputs An important issue in employing DEA is the selection of inputs and outputs. In order to calculate the efficiency and the score of each city entering this study the following outputs and inputs have been implemented: Inputs
X 1 - negative emigration percentage - the ratio between citizens that left the city to the total number of inhabitants (negative emigration ratio);
X 2 - percentage of unemployed citizens and obtaining minimal income insurance;
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International Symposium on Stochastic Models in Reliability Engineering, Life Sciences and Operations Management (SMRLO'10)
X 3 - percentage of deceased throughout the year; X 4 - average number of schoolchildren in a classroom;
X 5 - average number of apartments per citizen; X 6 - average spending by the local authority per citizen (in thousands NIS per citizen). Outputs
Y1 - positive immigration percentage - the ratio between citizens that joint the city to the total number of inhabitants (positive immigration ratio);
Y2 - average monthly income per citizen (in thousands NIS per month);
Y3 - percentage of successfully graduating from the city school system that complied with university entrance requirements;
Y4 - average number of private vehicles per citizen;
Y5 - average city income per citizen (including donations from the state). We will demonstrate the regarded procedure for Year 2008. The data on 70 cities with 5 outputs and 6 inputs are given in Table 1: Table 1. The numerical data for 2008 City
Year
X1
X2
X3
X4
X5
X6
Y1
Y2
Y3
Y4
Y5
Umm el-Faheim 2008 0.41% 16.21% 0.30% 30.25 0.28 4107.84 0.11% 3588.11 23.00% 0.1977 12924.81 OFAKIM
2008 3.77% 14.35% 0.55% 20.91 0.24 5863.73 0.09% 4182.77 37.60% 0.1604 17231.31
Or Yehuda
2008 3.53% 5.73% 0.49% 25.19 0.30 6250.42 0.11% 5706.27 43.60% 0.3121 20275.02
Or Akiva
2008 3.89% 8.03% 0.88% 21.25 0.31 6461.46 0.08% 4445.78 43.60% 0.2429 20919.81
Eilat
2008 10.99% 5.12% 0.32% 25.94 0.35 13736.39 0.10% 5334.78 51.80% 0.2974 39797.78
Ariel
2008 4.76% 3.51% 0.44% 27.52 0.28 6098.48 0.07% 5480.70 39.90% 0.2406 20728.72
Ashdod
2008 2.37% 8.54% 0.57% 26.61 0.29 5156.99 0.10% 5590.69 46.50% 0.1952 17595.95
Ashkelon
2008 2.84% 11.52% 0.69% 28.62 0.32 4692.72 0.10% 4989.72 49.40% 0.2343 16448.67
BakaJat
2008 0.76% 4.28% 0.34% 30.89 0.23 15958.20 0.08% 4275.78 41.00% 0.2457 55935.87
Beer-Sheva
2008 3.46% 10.95% 0.68% 26.22 0.37 5711.99 0.06% 5515.36 43.60% 0.2252 19125.60
Beit-Shean
2008 2.54% 9.35% 0.51% 20.99 0.28 9391.22 0.10% 4530.72 42.20% 0.2471 23928.66
Beit-Shemesh
2008 3.37% 4.07% 0.27% 24.07 0.22 3904.86 0.13% 5187.96 31.30% 0.1227 13059.96
Beitar-Illit
2008 2.49% 4.11% 0.10% 23.42 0.19 4100.62 0.19% 3345.32 25.30% 0.0523 10698.04
Bney-Brak
2008 3.74% 4.25% 0.46% 25.73 0.26 5249.03 0.08% 4613.07 36.00% 0.5272 17272.95
Bat-Yam
2008 4.73% 5.73% 0.99% 26.37 0.37 5314.27 0.09% 4755.76 42.50% 0.2486 17487.41
Givatayim
2008 6.40% 1.76% 0.92% 30.63 0.45 6798.70 0.11% 8775.23 66.30% 0.3988 21178.30
Dimona
2008 3.19% 15.87% 0.70% 24.51 0.33 5676.74 0.06% 5677.29 35.70% 0.1778 18799.31
Hod-Hasharon 2008 3.74% 1.42% 0.36% 28.36 0.31 6234.17 0.14% 9580.47 66.10% 0.3808 20975.07 Herzliya
2008 4.48% 1.90% 0.70% 27.34 0.39 8773.56 0.09% 8637.24 64.10% 0.4884 29958.56
Hadera
2008 3.06% 5.82% 0.75% 26.32 0.34 6128.19 0.10% 5492.21 44.60% 0.2937 19964.86
Holon
2008 3.67% 3.46% 0.72% 27.65 0.36 5580.70 0.09% 6013.82 53.10% 0.3474 18974.67
Haifa
2008 3.18% 7.38% 0.99% 25.49 0.42 8035.95 0.08% 7030.48 60.00% 0.3541 26247.90
Tiberias
2008 4.20% 12.19% 0.55% 24.13 0.35 8101.73 0.06% 4381.15 35.90% 0.2428 22693.33
Taibe
2008 0.34% 14.00% 0.38% 31.61 0.20 9559.56 0.13% 3898.18 30.90% 0.2393 26776.78
Tierra
2008 0.44% 3.60% 0.35% 28.73 0.25 3817.01 0.14% 3934.20 40.60% 0.2806 11242.56
Tirat-Carmel
2008 2.93% 10.66% 0.84% 22.98 0.33 7091.02 0.06% 4829.38 46.90% 0.2474 25790.75
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International Symposium on Stochastic Models in Reliability Engineering, Life Sciences and Operations Management (SMRLO'10) City
Year
X1
X2
X3
X4
X5
X6
Y1
Y2
Y3
Y4
Y5
Tamra
2008 0.44% 21.37% 0.33% 29.18 0.23 5344.81 0.11% 3621.48 36.30% 0.2158 16442.14
Yavne
2008 3.66% 6.82% 0.42% 26.17 0.28 6130.53 0.07% 6679.61 51.70% 0.3398 22593.32
Yehud
2008 4.30% 2.25% 0.48% 28.56 0.32 10237.37 0.10% 8353.91 61.50% 0.3870 26502.27
Jerusalem
2008 2.35% 3.66% 0.44% 26.23 0.25 4900.07 0.06% 5699.61 31.60% 0.2057 15893.69
Kfar-Saba
2008 4.13% 1.95% 0.68% 28.27 0.31 6634.08 0.09% 7856.73 68.10% 0.4168 20607.02
Karmiel
2008 3.49% 6.95% 0.68% 27.16 0.34 4962.59 0.09% 5732.54 51.80% 0.2510 17681.90
Lod
2008 4.09% 9.07% 0.69% 25.79 0.30 4856.54 0.07% 5015.39 37.10% 0.4340 16640.97
Migdal-Haemeq 2008 3.37% 10.14% 0.66% 23.05 0.32 7704.21 0.06% 4805.62 37.80% 0.2241 23104.41 Modiin
2008 3.59% 1.23% 0.13% 29.86 0.28 6999.50 0.23% 9856.76 74.30% 0.2941 17710.30
Maale-Adummim 2008 3.36% 2.78% 0.23% 27.71 0.26 5552.77 0.19% 6398.11 59.40% 0.2623 18134.97 Ma’alot Tarshiha 2008 3.13% 9.39% 0.51% 25.94 0.30 5882.31 0.08% 5169.07 45.70% 0.2417 19837.36 Nahariya
2008 3.61% 8.01% 0.76% 27.31 0.36 5422.02 0.09% 6357.79 54.00% 0.2948 17830.30
Ness-Ziona
2008 2.98% 3.44% 0.56% 28.02 0.33 7315.87 0.25% 8289.72 55.80% 0.3527 24775.00
Nazareth
2008 1.96% 12.21% 0.37% 29.79 0.28 4128.86 0.04% 4355.33 42.90% 0.2844 13355.96
Nazareth-Illit
2008 3.45% 10.89% 0.98% 24.88 0.39 5265.44 0.07% 4782.66 50.00% 0.2413 18210.00
Nesher
2008 5.42% 6.20% 0.65% 27.01 0.42 7332.59 0.08% 6431.81 62.90% 0.3021 24611.84
Netivot
2008 4.30% 11.45% 0.34% 22.59 0.25 5861.29 0.09% 4054.92 33.00% 0.1681 18952.17
Netanya
2008 2.51% 7.29% 0.80% 26.80 0.35 5559.58 0.11% 5564.58 45.20% 0.2623 18538.35
Skhnen
2008 0.56% 18.27% 0.24% 31.15 0.24 5999.12 0.10% 3836.95 37.10% 0.2295 15653.16
Akko
2008 3.00% 17.49% 0.72% 25.99 0.33 6689.17 0.07% 4503.33 35.10% 0.2142 21268.37
Afula
2008 3.08% 8.84% 0.60% 24.36 0.36 7129.49 0.09% 4758.94 45.00% 0.2606 22146.03
Arad
2008 4.95% 9.87% 0.83% 23.61 0.37 5793.13 0.08% 5686.36 48.10% 0.2074 19617.81
Petah-Tikva
2008 2.98% 3.36% 0.68% 26.32 0.35 6035.23 0.15% 6473.14 52.80% 0.6057 20679.46
Zfat
2008 8.03% 13.13% 0.65% 23.04 0.34 6214.73 0.04% 4377.43 30.60% 0.1903 19933.67
Qalansuwa
2008 0.53% 12.99% 0.26% 32.89 0.18 3428.85 0.11% 3866.99 27.90% 0.1958 9909.31
Kiryat- Ono
2008 4.48% 1.78% 0.59% 29.81 0.38 6755.53 0.14% 9339.45 61.30% 0.3952 21758.02
kiryat-ata
2008 3.15% 8.42% 0.77% 26.02 0.36 6070.42 0.10% 5749.87 45.90% 0.2808 20550.04
Qiryat-Bialik
2008 5.06% 6.71% 0.98% 28.92 0.40 5310.60 0.09% 6339.89 49.10% 0.3205 18057.01
Qiryat-Gat
2008 3.27% 12.51% 0.70% 25.30 0.31 6117.45 0.07% 4283.38 46.00% 0.1921 21587.22
Qiryat-Yam
2008 4.99% 11.57% 1.09% 26.24 0.39 5526.85 0.06% 5020.33 38.00% 0.2246 18136.94
Kiriat-Motzkin
2008 4.88% 6.53% 0.83% 30.82 0.37 4963.27 0.09% 6567.83 53.80% 0.2832 17301.74
kiryat-malchy
2008 4.02% 16.59% 0.40% 23.68 0.28 9024.10 0.07% 4001.12 29.10% 0.2242 26195.74
kiryat-shmona
2008 3.79% 7.56% 0.56% 23.22 0.35 8378.68 0.07% 4843.79 43.40% 0.2830 24846.45
Rosh-Haayin
2008 3.25% 3.14% 0.35% 27.73 0.27 6932.40 0.11% 7142.81 50.70% 0.3206 22670.03
Rishon Lezion
2008 3.30% 3.95% 0.55% 28.48 0.31 4757.82 0.10% 7072.96 54.60% 0.3509 17637.87
Rahat
2008 0.49% 28.86% 0.27% 30.92 0.08 4028.05 0.17% 3584.18 24.70% 0.1333 12866.80
Rehovot
2008 3.90% 5.64% 0.63% 27.88 0.35 5655.50 0.10% 6996.33 50.20% 0.3036 19575.62
Ramla
2008 3.54% 7.09% 0.63% 25.46 0.27 5155.45 0.06% 4692.08 36.10% 0.2588 17390.87
Ramat-Gan
2008 5.47% 2.31% 0.89% 27.10 0.43 6174.25 0.10% 7621.22 65.60% 0.3820 22463.48
Ramat-Hasharon 2008 4.37% 1.20% 0.54% 27.56 0.36 9373.42 0.11% 10676.27 69.20% 0.4843 31185.27 Raanana
2008 4.59% 1.23% 0.45% 27.94 0.29 7383.13 0.08% 10102.80 70.00% 0.3767 27198.43
Sderot
2008 5.28% 10.38% 0.68% 21.52 0.32 7895.45 0.06% 4417.50 40.90% 0.2264 25164.65
Shefaram
2008 0.62% 17.28% 0.35% 31.09 0.24 4319.61 0.15% 4272.76 42.20% 0.2464 14148.12
Tel-Aviv
2008 5.45% 4.20% 0.93% 24.14 0.47 10503.32 0.10% 7780.98 58.40% 0.5925 35566.68
Umm el-Faheim 2007 0.52% 16.49% 0.27% 30.36 0.28 4232.17 0.07% 3503.46 30.10% 0.1942 9168.60 OFAKIM
2007 3.84% 14.81% 0.68% 21.18 0.25 5765.02 0.08% 4226.35 31.00% 0.1550 11569.14
Or Yehuda
2007 3.38% 6.33% 0.61% 25.14 0.31 6571.42 0.12% 5478.12 37.20% 0.3148 13865.64
Or Akiva
2007 3.81% 11.68% 0.64% 22.02 0.30 6749.95 0.08% 4194.08 41.80% 0.2368 13992.22
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International Symposium on Stochastic Models in Reliability Engineering, Life Sciences and Operations Management (SMRLO'10) City
Year
X1
X2
X3
X4
X5
X6
Y1
Y2
Y3
Y4
Y5
Eilat
2007 10.49% 5.45% 0.38% 25.74 0.34 9775.43 0.11% 5150.50 49.30% 0.2864 22091.07
Ariel
2007 4.10% 3.66% 0.43% 26.77 0.27 6054.18 0.09% 5243.58 42.60% 0.2378 14106.72
Ashdod
2007 2.36% 9.72% 0.59% 26.48 0.29 4758.08 0.11% 5091.81 47.60% 0.1932 12479.80
Ashkelon
2007 2.55% 13.87% 0.74% 28.88 0.31 4781.68 0.10% 4780.43 46.80% 0.2312 11688.01
BakaJat
2007 0.55% 8.54% 0.35% 31.34 0.24 4643.00 0.13% 4365.51 41.50% 0.2409 8989.90
Beer-Sheva
2007 3.20% 12.08% 0.69% 26.41 0.37 5514.61 0.06% 5620.23 43.10% 0.2243 12955.26
Beit-Shean
2007 2.91% 10.29% 0.49% 21.24 0.28 9637.81 0.09% 4624.84 35.10% 0.2393 15766.02
Beit-Shemesh
2007 3.09% 4.96% 0.25% 24.27 0.23 4466.11 0.16% 4912.60 32.50% 0.1267 9050.65
Beitar-Illit
2007 2.50% 4.42% 0.08% 22.39 0.18 4823.16 0.20% 3197.23 32.50% 0.0533 6332.90
Bney-Brak
2007 3.74% 4.24% 0.48% 25.66 0.26 5173.50 0.08% 4514.19 32.50% 0.4731 11729.91
Bat-Yam
2007 4.59% 6.08% 1.04% 26.40 0.37 4958.59 0.08% 4586.62 43.60% 0.2466 11771.83
Givatayim
2007 6.10% 1.96% 1.05% 30.92 0.45 5998.44 0.12% 8259.25 66.60% 0.4071 13700.92
Dimona
2007 3.62% 17.95% 0.69% 24.59 0.33 5903.85 0.06% 5677.53 34.10% 0.1725 12518.99
Hod-Hasharon 2007 3.40% 1.69% 0.45% 28.69 0.31 5959.08 0.15% 8854.76 65.60% 0.3821 13155.74 Herzliya
2007 4.43% 1.99% 0.64% 27.40 0.39 7836.23 0.08% 8076.68 65.00% 0.5061 18810.79
Hadera
2007 3.08% 7.98% 0.69% 26.08 0.34 5741.28 0.09% 5301.80 45.60% 0.2895 13346.27
Holon
2007 3.67% 3.78% 0.75% 27.83 0.36 5003.69 0.09% 5678.08 48.80% 0.3517 12403.61
Haifa
2007 3.21% 7.98% 0.98% 25.75 0.42 7618.54 0.07% 6938.97 58.90% 0.3502 17267.25
Tiberias
2007 3.94% 12.62% 0.56% 24.46 0.35 6387.78 0.06% 4438.59 36.70% 0.2402 14632.41
Taibe
2007 0.40% 13.75% 0.34% 31.72 0.20 5383.81 0.12% 3938.88 32.50% 0.2290 4700.83
Tierra
2007 0.35% 4.15% 0.37% 28.66 0.25 4194.86 0.10% 4181.62 36.90% 0.2668 8477.00
Tirat-Carmel
2007 2.91% 11.68% 0.73% 22.31 0.33 7304.29 0.08% 4710.22 46.40% 0.2462 18785.79
Tamra
2007 0.50% 23.63% 0.23% 29.03 0.22 4873.81 0.12% 3621.66 42.90% 0.2131 9692.01
Yavne
2007 3.48% 7.40% 0.42% 26.78 0.27 6023.27 0.07% 6491.69 52.70% 0.3390 15322.93
Yehud
2007 4.00% 2.38% 0.49% 29.09 0.32 5833.91 0.08% 7496.08 58.10% 0.3859 13361.17
Jerusalem
2007 2.25% 4.27% 0.46% 26.18 0.26 5272.54 0.06% 5575.72 31.50% 0.2034 11294.58
Kfar-Saba
2007 3.69% 2.20% 0.59% 28.36 0.31 5645.17 0.10% 7502.91 65.40% 0.4124 13044.66
Karmiel
2007 3.82% 7.98% 0.69% 27.07 0.34 4790.15 0.08% 5664.58 49.20% 0.2502 11648.05
Lod
2007 4.08% 9.85% 0.65% 25.56 0.30 5331.43 0.06% 4720.34 38.40% 0.4202 12376.37
Migdal-Haemeq 2007 3.35% 11.08% 0.58% 22.64 0.32 5887.32 0.05% 4735.26 40.10% 0.2219 13558.24 Modiin
2007 3.35% 1.31% 0.09% 29.45 0.29 4988.70 0.28% 9280.00 76.70% 0.2987 11201.16
Maale-Adummim 2007 3.44% 2.59% 0.23% 27.49 0.26 5555.60 0.16% 6490.48 59.10% 0.2645 12036.37 Ma’alot Tarshiha 2007 2.90% 10.58% 0.55% 24.86 0.30 5747.82 0.09% 4989.13 45.80% 0.2367 12891.54 Nahariya
2007 3.86% 8.47% 0.88% 26.69 0.36 5404.66 0.10% 6190.95 53.00% 0.2937 11349.63
Ness-Ziona
2007 2.75% 4.36% 0.49% 27.55 0.32 7491.69 0.24% 7556.07 55.00% 0.3565 16905.03
Nazareth
2007 2.17% 18.49% 0.37% 29.67 0.28 3942.81 0.05% 4383.34 42.00% 0.2739 8725.22
Nazareth-Illit
2007 3.51% 13.06% 0.91% 26.05 0.39 5431.68 0.07% 4917.52 47.00% 0.2362 11834.19
Nesher
2007 4.41% 6.77% 0.68% 27.19 0.41 6286.14 0.09% 6251.48 60.70% 0.2994 14693.95
Netivot
2007 4.33% 12.97% 0.43% 22.56 0.26 5736.80 0.09% 3983.00 33.20% 0.1611 11997.82
Netanya
2007 2.61% 8.30% 0.80% 27.19 0.35 4993.63 0.10% 5241.44 43.90% 0.2584 12054.83
Skhnen
2007 0.51% 19.13% 0.28% 31.51 0.21 5662.27 0.11% 3753.30 37.10% 0.2223 10697.09
Akko
2007 2.88% 18.51% 0.78% 25.73 0.33 5346.91 0.07% 4531.23 37.10% 0.2102 12467.09
Afula
2007 3.12% 9.88% 0.65% 25.08 0.36 6248.25 0.09% 5077.78 46.70% 0.2579 12842.25
Arad
2007 5.30% 13.51% 0.75% 23.64 0.37 5901.65 0.06% 5531.71 50.20% 0.2084 12458.49
Petah-Tikva
2007 3.01% 3.25% 0.67% 26.49 0.35 5800.08 0.12% 6219.70 53.30% 0.5726 13728.57
Zfat
2007 5.51% 12.53% 0.62% 23.50 0.34 6438.91 0.07% 4427.93 32.80% 0.1839 13103.47
Qalansuwa
2007 0.48% 13.77% 0.25% 32.78 0.18 3460.11 0.15% 4093.00 27.80% 0.1903 6705.55
Kiryat- Ono
2007 4.28% 1.99% 0.67% 29.35 0.38 6819.38 0.13% 8539.01 63.20% 0.3971 14937.99
416
International Symposium on Stochastic Models in Reliability Engineering, Life Sciences and Operations Management (SMRLO'10) City kiryat-ata
Year
X1
X2
X3
X4
X5
X6
Y1
Y2
Y3
Y4
Y5
2007 3.07% 9.24% 0.75% 26.65 0.36 5536.75 0.10% 5572.76 46.70% 0.2775 13507.75
Qiryat-Bialik
2007 4.86% 7.61% 0.85% 29.52 0.40 5137.21 0.09% 6257.44 46.90% 0.3180 11811.60
Qiryat-Gat
2007 3.67% 13.80% 0.66% 25.18 0.31 6192.98 0.05% 4189.56 43.20% 0.1897 14900.79
Qiryat-Yam
2007 4.83% 12.47% 1.12% 26.91 0.39 5721.28 0.07% 5010.57 35.20% 0.2218 12345.43
Kiriat-Motzkin
2007 4.63% 7.14% 0.87% 30.98 0.37 4721.07 0.11% 6451.54 49.80% 0.2815 11689.02
kiryat-malchy
2007 4.34% 17.79% 0.61% 23.76 0.29 7686.50 0.07% 3920.29 29.90% 0.2186 15440.64
kiryat-shmona
2007 3.69% 8.20% 0.58% 24.08 0.35 7867.33 0.07% 4830.48 51.20% 0.2725 15627.54
Rosh-Haayin
2007 3.32% 3.45% 0.28% 27.07 0.27 6189.53 0.10% 6907.95 53.70% 0.3202 14317.89
Rishon Lezion
2007 3.23% 4.24% 0.55% 28.20 0.31 4800.22 0.10% 6620.68 55.60% 0.3494 12667.93
Rahat
2007 0.66% 29.91% 0.30% 30.84 0.08 3721.42 0.07% 3596.92 26.40% 0.1303 8398.82
Rehovot
2007 3.77% 6.61% 0.65% 27.94 0.35 6453.53 0.10% 6751.53 54.40% 0.3044 13353.42
Ramla
2007 3.78% 8.19% 0.67% 25.72 0.27 8669.89 0.06% 4459.08 33.50% 0.2541 14344.04
Ramat-Gan
2007 5.38% 2.62% 0.92% 26.75 0.44 6128.87 0.10% 7211.83 64.90% 0.3841 15008.28
Ramat-Hasharon 2007 4.20% 1.39% 0.52% 27.82 0.36 9199.04 0.10% 10041.18 71.10% 0.4964 21141.94 Raanana
2007 4.08% 1.42% 0.42% 27.92 0.30 7856.34 0.10% 9419.10 68.20% 0.3788 17121.83
Sderot
2007 4.59% 13.26% 0.64% 21.38 0.32 9007.15 0.08% 4264.63 36.60% 0.2197 19469.61
Shefaram
2007 0.74% 18.79% 0.34% 30.80 0.24 4376.51 0.15% 4372.88 36.70% 0.2429 9638.01
Tel-Aviv
2007 4.95% 4.66% 0.99% 24.25 0.47 9952.09 0.12% 7275.70 56.10% 0.5826 24263.23
Umm el-Faheim 2006 0.58% 16.96% 0.29% 29.60 0.26 4031.74 0.07% 3355.61 23.00% 0.1832 3973.11 OFAKIM
2006 3.97% 15.43% 0.55% 21.93 0.25 6140.57 0.09% 4021.56 25.30% 0.1502 5746.55
Or Yehuda
2006 3.91% 6.78% 0.62% 24.89 0.31 5717.50 0.12% 5557.37 37.20% 0.3075 5401.72
Or Akiva
2006 3.92% 13.33% 0.58% 22.99 0.30 7337.37 0.09% 4124.33 35.60% 0.2324 6592.19
Eilat
2006 11.45% 5.42% 0.32% 25.13 0.35 8831.58 0.10% 5170.14 46.80% 0.2827 9009.97
Ariel
2006 5.31% 4.08% 0.46% 27.02 0.27 5536.68 0.07% 5306.77 42.40% 0.2352 5278.97
Ashdod
2006 2.35% 10.73% 0.59% 26.41 0.29 4720.83 0.13% 5168.95 44.90% 0.1903 4535.28
Ashkelon
2006 3.10% 15.67% 0.71% 29.05 0.32 4345.39 0.09% 4645.88 48.10% 0.2276 4373.55
BakaJat
2006 0.71% 9.53% 0.26% 31.44 0.23 4919.84 0.11% 3900.28 36.50% 0.2287 4234.01
Beer-Sheva
2006 3.55% 15.19% 0.71% 25.73 0.37 5368.67 0.07% 5467.78 41.30% 0.2214 5229.46
Beit-Shean
2006 3.70% 11.19% 0.42% 21.38 0.28 7908.85 0.04% 4329.42 35.00% 0.2359 6270.90
Beit-Shemesh
2006 3.62% 5.43% 0.27% 24.48 0.24 4493.94 0.20% 5016.11 34.90% 0.1304 4245.61
Beitar-Illit
2006 3.37% 4.68% 0.09% 22.34 0.19 4761.60 0.17% 3256.01 4.50% 0.0544 4532.36
Bney-Brak
2006 4.41% 4.50% 0.48% 25.01 0.26 5198.57 0.08% 4552.57 7.80% 0.4267 4694.89
Bat-Yam
2006 5.68% 7.05% 0.96% 26.12 0.37 4571.60 0.07% 4638.47 43.20% 0.2424 4596.63
Givatayim
2006 7.01% 2.23% 1.01% 29.67 0.46 5702.59 0.11% 8269.47 67.00% 0.4086 5315.72
Dimona
2006 3.84% 20.47% 0.77% 24.83 0.33 5711.13 0.05% 5330.98 37.70% 0.1653 5294.57
Hod-Hasharon 2006 3.81% 1.79% 0.41% 28.86 0.32 6273.68 0.16% 8823.08 62.60% 0.3808 6029.56 Herzliya
2006 4.86% 2.19% 0.65% 27.51 0.39 7273.56 0.08% 7997.90 65.00% 0.4821 7535.40
Hadera
2006 3.53% 9.50% 0.75% 26.36 0.34 5375.72 0.09% 5162.32 40.90% 0.2830 5235.46
Holon
2006 4.38% 4.39% 0.72% 27.70 0.35 4967.89 0.08% 5718.21 47.50% 0.3571 5035.63
Haifa
2006 3.48% 8.53% 0.95% 25.96 0.41 7408.64 0.08% 6643.68 57.40% 0.3455 7508.53
Tiberias
2006 4.84% 13.74% 0.58% 23.28 0.35 7001.30 0.05% 4309.33 30.30% 0.2371 6715.83
Taibe
2006 0.64% 13.49% 0.26% 31.39 0.19 2906.52 0.08% 3550.05 28.10% 0.2192 2801.85
Tierra
2006 0.56% 4.50% 0.32% 28.10 0.25 4657.80 0.15% 3845.52 37.80% 0.2471 3653.06
Tirat-Carmel
2006 3.22% 12.39% 0.78% 23.18 0.33 6998.89 0.08% 4541.03 38.50% 0.2440 6937.71
Tamra
2006 0.53% 24.50% 0.36% 28.55 0.22 4644.45 0.10% 3427.45 38.70% 0.2023 4291.62
Yavne
2006 4.47% 8.01% 0.43% 27.68 0.27 6024.00 0.07% 6442.54 50.40% 0.3338 6110.68
Yehud
2006 4.69% 2.71% 0.56% 28.72 0.32 5899.54 0.09% 7613.75 57.50% 0.3860 5259.71
Jerusalem
2006 2.56% 4.49% 0.45% 25.86 0.26 4424.60 0.06% 5669.84 31.70% 0.2023 4321.84
417
International Symposium on Stochastic Models in Reliability Engineering, Life Sciences and Operations Management (SMRLO'10) City Kfar-Saba
Year
X1
X2
X3
X4
X5
X6
Y1
Y2
Y3
Y4
Y5
2006 3.94% 2.41% 0.60% 28.72 0.31 5668.50 0.10% 7544.79 65.30% 0.4167 6345.94
Karmiel
2006 3.54% 8.72% 0.66% 27.13 0.33 5069.12 0.11% 5434.60 48.30% 0.2459 5260.46
Lod
2006 5.09% 10.83% 0.61% 25.16 0.30 5035.33 0.06% 4800.29 34.70% 0.4074 4427.78
Migdal-Haemeq 2006 3.40% 11.75% 0.64% 22.70 0.32 5876.33 0.07% 4505.44 36.50% 0.2216 5287.48 Modiin
2006 4.03% 1.33% 0.14% 30.21 0.30 5082.54 0.24% 9652.30 72.90% 0.3005 5016.07
Maale-Adummim 2006 3.53% 2.70% 0.31% 27.69 0.26 6173.08 0.22% 6565.38 55.70% 0.2652 6310.10 Ma’alot Tarshiha 2006 3.77% 11.21% 0.52% 25.30 0.30 6158.73 0.08% 4791.92 47.70% 0.2351 6012.77 Nahariya
2006 3.89% 9.04% 0.80% 27.70 0.36 5400.13 0.12% 6111.42 50.10% 0.2873 5429.66
Ness-Ziona
2006 3.35% 4.78% 0.50% 26.91 0.34 7458.10 0.21% 7484.89 55.20% 0.3497 7623.72
Nazareth
2006 1.78% 20.65% 0.34% 29.27 0.28 4140.83 0.07% 4198.90 40.00% 0.2626 3436.44
Nazareth-Illit
2006 3.73% 14.34% 0.93% 27.36 0.38 7506.09 0.08% 4621.52 51.00% 0.2303 7612.51
Nesher
2006 5.53% 7.30% 0.61% 26.68 0.41 6298.01 0.09% 6044.25 51.80% 0.2998 6909.04
Netivot
2006 4.21% 13.40% 0.40% 22.28 0.26 5400.69 0.11% 3759.65 26.30% 0.1582 5582.78
Netanya
2006 3.00% 9.15% 0.76% 27.18 0.35 4885.10 0.11% 5210.34 45.90% 0.2517 4812.54
Skhnen
2006 0.68% 19.65% 0.25% 31.02 0.21 4255.24 0.10% 3434.83 24.50% 0.2104 4294.47
Akko
2006 3.60% 19.09% 0.82% 25.02 0.32 5880.38 0.07% 4435.51 32.90% 0.2079 5215.99
Afula
2006 3.56% 11.49% 0.66% 24.96 0.36 5958.57 0.08% 4820.73 42.20% 0.2518 5931.07
Arad
2006 6.76% 22.37% 0.66% 23.24 0.36 5529.28 0.04% 5358.44 47.70% 0.2042 4854.75
Petah-Tikva
2006 3.41% 3.36% 0.71% 26.37 0.35 6125.10 0.11% 6206.13 53.00% 0.5408 5911.18
Zfat
2006 7.29% 13.38% 0.64% 23.32 0.35 6705.75 0.06% 4238.11 30.70% 0.1866 6778.28
Qalansuwa
2006 0.68% 13.76% 0.24% 31.90 0.19 3627.31 0.12% 3832.13 30.70% 0.1783 3448.67
Kiryat- Ono
2006 5.21% 2.21% 0.57% 29.28 0.38 6409.95 0.12% 8345.80 60.90% 0.3969 5982.21
kiryat-ata
2006 3.76% 9.79% 0.76% 26.21 0.36 5897.98 0.09% 5307.11 42.50% 0.2722 5691.01
Qiryat-Bialik
2006 5.60% 8.12% 0.87% 29.56 0.39 4860.59 0.08% 5926.38 50.10% 0.3141 4743.52
Qiryat-Gat
2006 4.04% 14.72% 0.66% 25.29 0.30 6221.10 0.05% 4254.37 43.30% 0.1839 5850.21
Qiryat-Yam
2006 5.40% 12.99% 1.04% 26.55 0.38 5169.58 0.07% 4782.72 40.60% 0.2194 4797.98
Kiriat-Motzkin
2006 5.47% 7.73% 0.87% 29.45 0.37 4507.54 0.08% 6109.22 50.50% 0.2846 4224.28
kiryat-malchy
2006 4.71% 18.84% 0.52% 23.61 0.29 7513.38 0.08% 3937.17 28.50% 0.2119 6970.30
kiryat-shmona
2006 4.25% 8.91% 0.52% 23.37 0.34 7824.78 0.08% 4613.46 42.30% 0.2677 7282.38
Rosh-Haayin
2006 3.95% 3.57% 0.34% 27.45 0.28 6158.39 0.09% 7009.25 48.10% 0.3143 6258.82
Rishon Lezion
2006 3.81% 4.70% 0.52% 28.34 0.31 4941.75 0.11% 6790.28 54.80% 0.3456 5211.72
Rahat
2006 0.78% 32.02% 0.35% 30.36 0.08 3369.27 0.09% 3621.49 16.30% 0.1230 3593.39
Rehovot
2006 3.96% 7.57% 0.73% 28.40 0.35 5818.41 0.12% 6736.51 52.30% 0.2984 5713.27
Ramla
2006 3.96% 9.31% 0.60% 26.60 0.27 5506.30 0.08% 4533.86 31.00% 0.2481 5131.61
Ramat-Gan
2006 6.22% 3.01% 0.87% 26.89 0.44 5935.48 0.10% 7191.15 63.20% 0.3875 5987.96
Ramat-Hasharon 2006 4.86% 1.42% 0.55% 27.69 0.36 7390.71 0.09% 9664.47 66.10% 0.5069 7373.36 Raanana
2006 4.72% 1.56% 0.47% 27.82 0.30 6437.40 0.09% 9269.74 68.40% 0.3848 6786.28
Sderot
2006 4.13% 15.51% 0.64% 21.61 0.32 7718.35 0.09% 4135.18 30.30% 0.2074 7083.78
Shefaram
2006 0.97% 19.29% 0.33% 30.99 0.24 5364.56 0.13% 4233.62 40.60% 0.2368 5057.73
Tel-Aviv
2006 5.52% 5.24% 0.97% 24.20 0.48 9785.80 0.12% 7208.46 55.70% 0.5957 9799.20
Table 2. Score and Malmquist productivity change index Cross Efficiency
Malmquist productivity
City
Umm elFaheim OFAKIM
2008
2007
2006
Mean
Rank
20062007
20072008
Mean
0.7547
0.7442
0.7667
0.755
54
0.777
0.561
0.660
0.7228
0.7201
0.7491
0.731
63
0.723
0.570
0.642
418
International Symposium on Stochastic Models in Reliability Engineering, Life Sciences and Operations Management (SMRLO'10) Cross Efficiency
Malmquist productivity
City 2008
2007
2006
Mean
Rank
20062007
20072008
Mean
Or Yehuda
0.8159
0.7957
0.7897
0.800
31
0.738
0.615
0.674
Or Akiva
0.7936
0.7644
0.7603
0.773
47
0.742
0.587
0.660
Eilat
0.7003
0.8116
0.793
0.768
49
0.631
0.546
0.587
Ariel
0.7957
0.8402
0.7509
0.796
35
0.724
0.528
0.618
Ashdod
0.8472
0.9064
0.7849
0.846
17
0.852
0.534
0.675
Ashkelon
0.8466
0.8264
0.7591
0.811
27
0.803
0.584
0.685
BakaJat
0.8778
0.7549
0.7564
0.796
33
0.406
0.644
0.511
Beer-Sheva
0.7977
0.8083
0.7616
0.789
39
0.752
0.548
0.642
Beit-Shean
0.6782
0.6852
0.717
0.693
68
0.696
0.504
0.592
Beit-Shemesh
0.8029
0.7389
0.7532
0.765
50
0.781
0.710
0.745
Beitar-Illit
0.6603
0.542
0.7139
0.639
69
1.018
0.669
0.826
Bney-Brak
0.8154
0.8219
0.7441
0.794
36
0.824
0.668
0.742
Bat-Yam
0.769
0.7696
0.7162
0.752
55
0.794
0.580
0.679
Givatayim
0.8018
0.811
0.7614
0.791
37
0.921
0.681
0.792
Dimona
0.781
0.7421
0.7246
0.749
56
0.701
0.572
0.633
Hod-Hasharon
0.9233
0.8963
0.8867
0.902
8
0.849
0.644
0.740
Herzliya
0.8883
0.9334
0.913
0.912
5
0.833
0.615
0.716
Hadera
0.8083
0.8322
0.7795
0.807
29
0.775
0.555
0.656
Holon
0.8495
0.8551
0.8034
0.836
20
0.833
0.611
0.713
Haifa
0.8436
0.8637
0.8707
0.859
16
0.828
0.613
0.712
Tiberias
0.6754
0.7921
0.7588
0.742
60
0.785
0.515
0.636
Taibe
0.7184
0.4331
0.7628
0.638
70
0.552
0.844
0.682
Tierra
0.8151
0.7819
0.73
0.776
45
0.944
0.608
0.758
Tirat-Carmel
0.8799
0.9465
0.8279
0.885
11
0.781
0.475
0.609
Tamra
0.782
0.7622
0.7889
0.778
44
0.869
0.573
0.705
Yavne
0.915
0.9477
0.8557
0.906
6
0.784
0.592
0.681
Yehud
0.7135
0.8669
0.792
0.791
38
0.847
0.642
0.738
Jerusalem
0.7832
0.7935
0.7899
0.789
40
0.779
0.606
0.687
Kfar-Saba
0.8421
0.893
0.9577
0.898
10
0.914
0.679
0.788
Karmiel
0.8669
0.8245
0.8146
0.835
21
0.802
0.581
0.682
Lod MigdalHaemeq
0.8172
0.811
0.7231
0.784
41
0.778
0.629
0.699
0.7331
0.8169
0.7389
0.763
52
0.792
0.526
0.646
0.7887
0.9351
0.9014
0.875
13
1.063
0.556
0.769
0.8798
0.851
0.9015
0.877
12
0.815
0.667
0.737
0.823
0.8187
0.8017
0.814
25
0.755
0.598
0.672
Modiin MaaleAdummim Ma’alot Tarshiha Nahariya
0.829
0.7635
0.8065
0.800
32
0.815
0.653
0.730
Ness-Ziona
0.9108
0.9168
0.9268
0.918
3
0.843
0.603
0.713
Nazareth
0.7881
0.7453
0.6936
0.742
59
0.852
0.650
0.744 0.692
Nazareth-Illit
0.829
0.7452
0.8145
0.796
34
0.739
0.647
Nesher
0.8327
0.8329
0.8452
0.837
19
0.832
0.616
0.716
Netivot
0.7583
0.734
0.7855
0.759
53
0.668
0.570
0.617
Netanya
0.8271
0.833
0.7818
0.814
26
0.787
0.554
0.661
Skhnen
0.686
0.7354
0.808
0.743
58
0.794
0.573
0.675
Akko
0.7486
0.7878
0.7028
0.746
57
0.750
0.487
0.604
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International Symposium on Stochastic Models in Reliability Engineering, Life Sciences and Operations Management (SMRLO'10) Cross Efficiency
Malmquist productivity
City 2008
2007
2006
Mean
Rank
20062007
20072008
Mean
Afula
0.7735
0.7568
0.7951
0.775
46
0.770
0.622
0.692
Arad
0.8106
0.7346
0.6671
0.737
62
0.783
0.624
0.699
Petah-Tikva
0.9157
0.9086
0.8788
0.901
9
0.846
0.653
0.743 0.613
Zfat
0.7006
0.6958
0.7388
0.712
66
0.659
0.571
Qalansuwa
0.7304
0.7151
0.7688
0.738
61
0.949
0.667
0.796
Kiryat- Ono
0.8552
0.8515
0.8136
0.840
18
0.823
0.645
0.728
kiryat-ata
0.8318
0.8541
0.7754
0.820
23
0.785
0.528
0.644
Qiryat-Bialik
0.8093
0.769
0.7334
0.771
48
0.786
0.637
0.707
Qiryat-Gat
0.834
0.828
0.7431
0.802
30
0.707
0.527
0.610
Qiryat-Yam
0.7454
0.7074
0.6776
0.710
67
0.672
0.565
0.616
Kiriat-Motzkin
0.8299
0.8101
0.7097
0.783
42
0.848
0.608
0.718
kiryat-malchy
0.6894
0.7275
0.7591
0.725
65
0.630
0.533
0.580
kiryat-Shmona
0.7394
0.7617
0.7934
0.765
51
0.809
0.630
0.714
Rosh-Haayin
0.8454
0.9006
0.8781
0.875
14
0.792
0.601
0.690
Rishon Lezion
0.9341
0.9419
0.8739
0.917
4
0.847
0.611
0.720
Rahat
0.7923
0.8102
0.8267
0.810
28
0.674
0.662
0.668
Rehovot
0.8574
0.7841
0.812
0.818
24
0.741
0.652
0.695
Ramla
0.7926
0.6538
0.7399
0.729
64
0.672
0.546
0.606
Ramat-Gan RamatHasharon
0.9114
0.8701
0.8126
0.865
15
0.822
0.649
0.730
0.9001
0.9564
0.9233
0.927
2
0.779
0.601
0.684
0.9631
0.9093
0.9432
0.939
1
0.791
0.612
0.695
Raanana Sderot
0.7598
0.8104
0.7684
0.780
43
0.786
0.469
0.607
Shefaram
0.8488
0.8041
0.8143
0.822
22
0.793
0.639
0.712
Tel-Aviv
0.8686
0.9401
0.9029
0.904
7
0.820
0.616
0.711
Mean
0.808
0.805
0.793
0.802
0.778
0.598
0.682
• Note that all Malmquist index averages are geometric means. • The results of Malmquist index from DEAP version 2.1 Table 3. 10 top ranked Israeli cities Malmquist productivity
Cross Efficiency
City 2008
2007
2006
Mean
Rank
20062007
20072008
Mean*
Raanana
0.9631
0.9093
0.9432
0.939
1
0.791
0.612
0.695
Ramat-Hasharon
0.9001
0.9564
0.9233
0.927
2
0.779
0.601
0.684
Ness-Ziona Rishon Lezion
0.9108 0.9341
0.9168 0.9419
0.9268 0.8739
0.918 0.917
3 4
0.843 0.847
0.603 0.611
0.713 0.720
Herzliya
0.8883
0.9334
0.913
0.912
5
0.833
0.615
0.716
Yavne
0.915
0.9477
0.8557
0.906
6
0.784
0.592
0.681
Tel-Aviv Hod-Hasharon
0.8686 0.9233
0.9401 0.8963
0.9029 0.8867
0.904 0.902
7 8
0.82 0.849
0.616 0.644
0.711 0.740
Petah-Tikva
0.9157
0.9086
0.8788
0.901
9
0.846
0.653
0.743
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International Symposium on Stochastic Models in Reliability Engineering, Life Sciences and Operations Management (SMRLO'10) Cross Efficiency
City
Kfar-Saba
Malmquist productivity
2008
2007
2006
Mean
Rank
20062007
20072008
Mean*
0.8421
0.893
0.9577
0.898
10
0.914
0.679
0.788
• Note that according to the Cross Efficiency method results Raanana, Ramat-Hasharon and Ness-Ziona turned out to be ranked first. The common feature of these cities is their geographical position in the centre of the country and along the sea coast line.
Table 4. 10 bottom ranked Israeli cities
Qalansuwa
Malmquist productivity
Cross Efficiency
City 2008
2007
2006
Mean
Rank
20062007
20072008
Mean*
0.7304
0.7151
0.7688
0.738
61
0.949
0.667
0.796
Arad
0.8106
0.7346
0.6671
0.737
62
0.783
0.624
0.699
Ofakim
0.7228
0.7201
0.7491
0.731
63
0.723
0.57
0.642
Ramla
0.7926
0.6538
0.7399
0.729
64
0.672
0.546
0.606
Kiryat-Mal'achy
0.6894
0.7275
0.7591
0.725
65
0.63
0.533
0.580
Zfat
0.7006
0.6958
0.7388
0.712
66
0.659
0.571
0.613
Qiryat-Yam
0.7454
0.7074
0.6776
0.71
67
0.672
0.565
0.616
Beit-Shean
0.6782
0.6852
0.717
0.693
68
0.696
0.504
0.592
Beitar-Illit
0.6603
0.542
0.7139
0.639
69
1.018
0.669
0.826
Taibe
0.7184
0.4331
0.7628
0.638
70
0.552
0.844
0.682
• Note that bottom ranked cities listed in Table 4 belong generally to the northern and southern outskirts of the country.
5. Conclusions and Future Research In this paper we intended to demonstrate an important application area of the DEA methodology enabling relative effectively assessment of DMUs in conjunction with the CE method to carry out fully ranking for the same, all this compared with the Malmquist productivity index capable of evaluating relative improvement of each DMU per every pair of consecutive time periods. These methods have been applied to evaluating 70 Israeli cities within years 2006, 2007 and 2008. The results obtained which have been reported in the present study may lead to the following conclusions: • No correlation whatsoever has been identified between the ranking position of the city and its relative improvement through years. As a matter of fact, the majority of cities investigated in our research show actually worsening rather than improvement, no matter whether being ranked at the top of the list or close to the bottom. • Ranking positions obtained as well as improvement rates refer of cause to the set of input / output criteria chosen for the research. A different choice of input / output criteria might cause other results, accordingly.
421
International Symposium on Stochastic Models in Reliability Engineering, Life Sciences and Operations Management (SMRLO'10) • There is no consistency within the ranking obtained on the basis of existing ranking methods. The substance of the ranking method is important for obtaining specific ranking results whatsoever. • No correlation whatsoever has been identified between the size of the city (number of inhabitants) and its ranking / relative improvement through years. In other words, one cannot claim those features to be size dependent. Ranking and improvement as reflected in our research relate to a broad spectrum of instances such as: education, health care, the local authority's municipal spending, etc. We suggest further research to be undertaken to estimate ranking of cities according to each criterion separately, while calculating relative weights for every criterion chosen. Then, efficiency score and ranking position for every participating city might be re-calculated with reference to the established weights. In addition, further investigation has to be undertaken as to specific reasons for cities' productivity worsening as detected in the framework of the current research.
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